Due to the complexity of the Continuous Vertical Datum for Canadian Waters (CVDCW) project, this will become clearer as I write more about it, it was necessary to form a (semi) multidisciplinary team to tackle the problems that the project faced. This team is comprised of the Canadian Hydrographic Service (CHS) and the Canadian Geodetic Survey (CGS).

The CVDCW combines the Canadian Gravimetric Geoid Model of 2013 (CGG2013), from the CGS, and ocean models of the sea surface topography, from the CHS, to obtain a Hydrographic Vertical Separation Surface (HyVSEP) that can reduce geodetic heights to a number of vertical water datums, primarily chart datum. This is done using eq. 1 where N is the geoid undulation from CGG2013, DOT is the Dynamic Ocean Topography, and sep(MSS-tidal level) is the difference between the Mean Sea Surface (MSS) and the tidal level or vertical water datum desired.

There are three measurements that therefore must be made to calculate the HyVSEP, all found on the right side of the equation. Each of these measurements, of course, have an uncertainty value associated with them, however, what Robin et al (2014) does not seem to address is that all three of these measurements for offshore modeling is reliant on *satellite altimetry*.

What then is satellite altimetry and how is it a key part in three separate measurements?

Typically, satellite altimetry is a form of microwave remote sensing (RADAR) that is found on special scientific satellites; SKYLAB, GEOS-3, SEASAT-1, Topex/Poseidon, GEOSAT, ERS-1&2, GFO, ENVISAT-1, Jason 1&2 (Jason 3 was launched January 2016 and has an altimeter); but is sometime found in the form of laser remote sensing particularly if polar regions are the target area; ICESat, Cryosat-2.

Unlike the InSAR method used in the RADARSAT missions, satellite altimetry is a nadir facing sensor which yields a much smaller footprint. Satellite altimetry can therefore achieve a much higher precision and accuracy because of the lower incident angle and through atmospheric corrections that are determined through measuring the atmospheric conditions with a Radiometer, which can only be utilized properly with a nadir sensor.

Image: JASON-2 satellite

There have been two different types of satellite altimetry missions, Geodetic Missions (GM) which has a non-repeating or very long repeat orbit, allowing for a more dense coverage and Exact Repeat Missions (ERM) which has a short repeat time and allows for the time modeling of time variant features. In total there has been 60 years of ERM data but less than 2.5 years of GM data as only ERS-1 and Geosat had GM orbits (Sanso and Sideris, 2013). This causes an issue for using satellite altimetry for geodetic purposes as the ERS-1 and Geosat altimetry data is not as accurate as modern altimetry data. The largest cause of this uncertainty is from the orbit determination of the satellite itself; Geosat used Doppler and ERS-1 used SLR (as well as PRARE until its malfunction early into the mission).

There has been effort to ‘re-process’ the data through remove-restore and crossover adjustment techniques which try to define a more accurate orbital model to the position of the satellite as well as combing the GM data with the more rigorous ERM data. I might have a future post that gets into more detail about this but for now it is just important to know that any surface solutions from satellite altimetry are a combination of GM and Interpolated ERM data.

There are many other considerations into determining accuracy that I won’t go into for this post but I do encourage you to check out the further readings if you are as interested in it as I am.

Now to get onto the meat of this post; how satellite altimetry is (probably) used simultaneously for all three measurements.

The first and most obvious measurement is in the tide models. Satellite altimetry measures the distance between the satellite and the instantaneous sea surface (Δh), averaged over time this produces a Mean Sea Surface (MSS) and can be used to determine various water level definitions such as LLWLT which is used for chart datum in Canada. A distinct advantage of satellite altimetry over its more traditional counterpart, tide gauges, is that the measurements are not in relationship to a fixed point but rather in relationship to the geo-center, the center of mass of the earth, which allows the data to be free from the effects of crustal motion.

The second measurement is the geoid measurement. The geoid, an equipotential surface, is a lumpy reference surface, also known as a datum, that represents Mean Sea Level (MSL). If the oceans where static then the geoid would coincide with the MSS but as they are dynamic they differ by a value called the *dynamic ocean topography *(DOT), ζ*.* The geoid undulation, N, is the separation value of the Geoid and the Ellipsoid and is used for terrestrial applications to convert geodetic heights to orthometric heights. For marine applications the geoid undulation is not useful on its own as it has no relation to the sea surface. Please read my post on the difference between using satellite gravimetry and satellite altimetry for geoid determination here.

As can be seen in the figure, the difference between the Ellipsoid and MSS can be calculated using the geoid undulation, N, and the DOT, ζ. The DOT is the third measurement that is needed for the HyVSEP. The DOT value can be reduced through the removal of tidal corrections (the first measurement), 75% of signal variance, and dynamic atmospheric corrections, 10% of signal value. The rest of the signal is from wind and other high frequency effects which can be modeled. The primary method of determining DOT, that I have read, is through the reduction of MSS and N, with N also being a function of DOT and MSS.

It has been my observation that all three measurements are co-dependent on each other so it will be interesting to see how the CHS and CGS handled this, but significantly more reading is required to fully understand how they’ve approached the problem so expect more posts on the matter in weeks to come.

Further Readings

SANSÒ, F., & SIDERIS, M. G. (2013). *Geoid determination: theory and methods.*

SEEBER, G. (2003). *Satellite geodesy: foundations, methods, and applications*. New York, Walter de Gruyter.

JASON MISSIONS

JASON-1: http://sealevel.jpl.nasa.gov/missions/jason1/jason1factsheet/

JASON-2: https://www.nasa.gov/mission_pages/ostm/spacecraft/index.html

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